Determining the impact of electrical loss in coaxial cable

Coaxial / radio frequency (RF) cables made of highly foamed polyethylene are widely used as antenna feeders, cabling of antenna arrays, equipment interconnections, mobile telecommunication systems, microwave transmission systems, broadcast transmission systems and other communication systems. Since the 1980s the operating frequency of cellular phones has continuously increased. In fact, many domestic and overseas telecommunication carriers are currently using a frequency of 2.5-2.6 GHz (4G). To meet the transmission requirements at high frequencies, RF cables require the use of highly foamed dielectric made with polymer resins which are as pure as possible, therefore with minimum polar groups attached to the polymer and minimum polar additives. In this paper, we compare rheology and dielectric loss properties of various Low Density Polyethylene (LDPE) gas injection compounds. Reduction of the attenuation of the coax cable is important since it can lead to increase in energy efficiency or reduction in cable weight, two desirable characteristics for cellular communication carriers. In this paper we model cable attenuation based on the differences in dielectric loss of LDPE resins and quantify the consequent increase in electrical power loss.

Typically, a high frequency cable is made by an inner conductor surrounded by a foamed insulation. In early attempts, the foaming step was implemented by compounding the polymer resin with a specific chemical foaming agent capable of blowing closed cells of desired size in the polymer. The issue with this approach is that the polymeric dielectric material traps residue of the foaming agent that deteriorate the dissipation factor (Df), also called tan and consequently the attenuation of the cable especially at the upper end of the frequency range. To overcome this, a physically foamed dielectric approach was developed based on injecting an inert gas (such as nitrogen, carbon dioxide) to blow the gas filled expanded cell. Adding a nucleating agent is a frequently used and effective technique to reduce cell size, enhance cell density and uniform cell distribution2.

Characteristics of the base polymer used to make the insulating material include good dissipation factor, Df (low Df), good extrudability and foaming capability and flexibility. Candidate materials are fluorocarbon polymer, polypropylene and polyethylene. Fluorocarbon polymers are expansive and polypropylene is stiff and difficult to foam. On other hand, polyethylene is cheap, has good electrical properties and is flexible. Therefore, it is a material of choice for insulation of coax cable. Generally, a blend of HDPE and LDPE resins is used. HDPE which has no or very little Long Chain Branching (LCB) provides good physical properties to the foam (stiffness, tensile strength, high temperature resistance)3. LDPE is selected because of its strain hardening and melt strength behaviors due to the presence of LCB and entanglement (as the deformation rate increases)4. These properties are crucial for foaming in order to prevent the melt from rupture and stabilize the bubble.

A small dissipation factor (for low signal loss) presupposes polyethylenes which are as pure as possible, i.e. with minimum polar groups5. Dissipation factor of polyethylene increases with decreasing density. This is because LDPE has side chains inducing dipole polarization6. HDPE has a few side chains resulting in dissipation factor values that are in general at least three times lower than LDPE. This is the reason why improvement of dissipation factor of LDPE component is crucial for low cable attenuation. The paper provides quantification of attenuation loss in coaxial / RF cable due to dissipation factor differences of available commercial grades of LDPE.

Rheology in foamingTo understand the importance of rheology in foaming, a simple bubble growth model from Newtonian fluid is useful. The model shows that the change in bubble radius R is proportional to the pressure difference inside (PD) and outside (Pc) the bubble and inversely proportional to the melt viscosity of the polymer ()7:

Here is the surface tension of the polymer.

The process of bubble growth is dictated by the magnitude of the viscosity. In fact, a balance between viscosity and elasticity dictates the bubble structure. It is desirable that the viscosity is low during the nucleation early stage of bubble growth (low ), increases gradually as the bubble grows further and becomes very high in the late stage of foaming (due to strain hardening behavior, melt strength, for example) to stabilize the foam structure. Higher degree of long-chain branching generally facilitates strain hardening behavior. Elasticity behavior (high recovery compliance) is desirable since it can prevent bubble collapse (due to viscous flow) at the exit of the die. Generally, narrow molecular weight distribution (MWD) polymers have a viscous dominating behavior.

About the authors Anny L Flory is a senior engineer in the Electrical & Telecommunications Unit of The Dow Chemical Company. She has a B.S. in Physics from Universitee Paul Sabatier in Toulouse France and a Ph.D. in Chemical Engineering from Texas Tech University. Her present research areas include gas injection polyolefin compounds and flame retardant technologies for wire and cable applications.

Chester J. Kmiec is a Development Leader for Wire and Cable Compounds group at the Dow Chemical Company. Chet has 36 years of experience in Polymer Applications Research an Development, the last 21 years at The Dow Chemical Company. He hold a B.S in Plastics Technology from Lowell Technological Institute and a M.B.A from the State University of New York at Buffalo.